I'm not 100% clear on what's so terrible about having the upper house composed of life-appointees selected by the executive and confirmed by the legislature. One of the few real powers that the Lords has is that it's the highest court in Britain. And the U.S. Supreme Court is composed of life-appointees selected by the executive and confirmed by the legislature. Again: what's so terrible?

I do think bicameralism is a good thing, and that the upper house should represent a social compact among social groups among whom rough consensus is needed for the social organism to remain healthy. At America's founding, those groups were preeminently the states, who considered themselves independently sovereign. In Britain, historically, the Lords represented the landed interest and the hereditary principle. I've argued in the past for a corporatist bicameralism for Israel, an appointed upper house (appointees to serve long, but not life terms) representing various sectors of society (and possibly even the disapora community), with very limited powers similar to Britain's Lords. (This would provide an alternative forum for hammering out social consensus versus the current mechanism of having narrow interest-group parties extort concessions in the coalition-building process in a proportional-rep parliament).

As for Britain, the weakness of their democracy is lack of direct accountability. Their executive is elected from the legislature, and their head of state is hereditary. They already have district-based elections to the legislature on a first-past-the-post basis. So if they wanted to experiment with creating a body that directly affects the "will of the people," how about the following compromise:

Lords would serve for lengthy fixed single terms - say, 10 years. 20% of the Lords would retire every two years, at which point the government and opposition would each select a "slate" of proposed replacements replacements. The slates would be presented to the British populace for preference voting, and the first x to clear the necessary vote hurdle through the preference system would be elected. The selection of slates would preserve the Commons' current role in selecting new Lords, reaffirming the supremacy of the Commons. The provision of a slate for the opposition would ensure that the government wouldn't simply "pack" its slate with undistinguished yes-men, and would give the people an opportunity to express disapproval of a government without really tipping the balance of power every two years. The preference system would incline the system towards producing outcomes that reflect social consensus - candidates would have to either be very popular with significant but narrow constituencies or broadly popular among the whole nation in order to get in. The result should be a natural check on the Commons, which, particularly in a system without a written Constitution, magnifies narrow electoral pluralities into decisive legislative majorities and scure governments with near-dictatorial powers.